Analytical Model of the Canonical 3D Helical Solenoid, for Efficient Computation of the Dynamic Electromagnetic Fields in Near- and Far-Field Regions, Complex Inductance, and Radiation Resistance

Abstract

<p> The recent work in [1] presented a novel analytical model for estimating the 3-dimensional (3D) magneto quasi-static (MQS) fields of the cylindrical solenoid with helical wire winding, using the \textit{static} Green's function and relying on the \textit{Schur} vector product of the electric current source vector and its tangent.</p> <p> </p> <p> In this work, we use the \textit{dynamic} Green's function to extend the model in [1] resulting in a frequency-dependent magnetic vector potential $\vec{A}(\omega)$. We derive expressions for efficient computation of all cylindrical components of the magnetic flux density vector $\vec{B}(\omega)$ as a function of the solenoid's geometric and material parameters. $\vec{A}(\omega)$ may be used to efficiently compute the frequency-dependent flux linkage $\Psi(\omega)$, the complex inductance $L(\omega)$, and the radiation patterns of the solenoid anywhere in 3D space including both near-field and far-field regions, excluding the (source) regions of conducting wire. Additionally, we propose the complex calibration coefficient $\chi(\omega)$ to account for the finite-radius conductor.</p> <p> </p> <p> Several numerical examples are provided to validate the proposed helical model against the superposition of circular loops. The proposed model is demonstrated across a wide spectrum from 60 Hz to 70 GHz, representing a wide range of applications that include low-frequency power systems to high-frequency mm-wave communication systems.</p>